1 1 3 ABCD ABD AC BD E E BD 1 : 2 (1) AB = AD =, AB AD = (2) AE = AB + (3) A F AD AE 2 = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD 1 1

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あおいじゅふく
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1 ABCD ABD AC BD E E BD : () AB = AD =, AB AD = () AE = AB + () A F AD AE = AF = AB + AD AF AE = t AC = t AE AC FC = t = (4) ABD ABCD AB + AD AB AD AB + AD AB AD

2 () AB sin π = AB = ABD AD = AB AD = cos π () E BD : AE = AB + = AD AE = 9 AB + AD = 9 (4 AB + 4 AB AE + AE ) = 9 (4 + + ) = 7 9 () BD M AMF AM = ( AB + AD) AM = AB sin π = AF = AF AM AF AF = AM = ( AB + AD) AF AE = ( AB + ( AD) AB + = 9 ( AB + AD) ( AB + AD) ) AD A = 9 ( AB + AB AD + AD ) = AF AC FCt =\ AC FC = AC ( AC AF) = B E M D AE (t AE AF) = t AE AE AF = C F 7 9 t =... t = 9 7 (4) ABD AB AD sin π = 4 7 ABCD ABD 9 7 = 9 CE : AE = : 7 BCD ABD

3 A B n n A a n b n c n () a = b = () n a n + b n + c n = a n+ = b n b n+ = a n + b n + c n () ABC b n b n+ + Ab n+ Bb n = C () A = B = C = () p n = b n x p n+ + Ap n+ Bp n = x = α, β (α < β) (p n+ αp n+ ) = β(p n+ αp n ) α = β = n b n = α n + β n + lim n b n =

4 a n + b n + c n a n + b n + c n αn + βn + 5 αn + 5 βn + 5 5

5 (a), (b), (c) n a n, b n, c n (b) A B A B A B (a) (b) (c) () (b) A B (a) a = = A, B A, B (b) b = + = () n (a), (b), (c) a n + b n + c n = a n+ = b n b n+ = a n + b n + c n (),, {b n } b n+ = a n+ + b n+ + c n+ = a n+ + b n+ + ( a n+ b n+ ) c n+ = a n+ b n+ = a n+ b n+ + = b n b n+ + = b n+ + b n + b n+ + b n+ b n = () b n+ + Ab n+ Bb n = C A =, B =, C = () p n = b n x b n = p n + x b n+, b n+, b n (p n+ + x) + (p n+ + x) (p n + x) = p n+ + p n+ p n = 9 x p n+ + Ap n+ Bp n = 9 x =

6 x = 5 {p n } p n+ + p n+ p n = p, p ( ) (a, b, c ) =,, b = a + b + c = p = b x = 5 =, p = b x = 5 = 7, p n+ + p n+ = ( p n+ + ) p n p n+ p n+ = ( p n+ ) p n, α =, β = p n+ + p n = p n+ p n = ( p + ) ( p ( p ) ( p ) n = ( ) n = ) n = ( ) n = ( ( ) n ) n p n = ( ) n + ( ) n = βn + αn lim n αn = lim n βn = lim n b n = 5... p n = αn + 5 βn = b n 5... b n = αn + 5 βn + 5

7 n n k a k ( < = k < = n) a, a, a,, a n P n ()() (4) {b k } ( < = k < = n) a k < = b k = a k a k > = 4 b k = n b k q n k= q =, q = q n n q n = n +

8 < = t < = π O A (cos t, sin t) O A t P P (f(t), g(t)) () OP = OA + AP f(t) = cos t cos t g(t) = sin t sin t + () t = a f(t) cos a = f(a) = () < c < π t = c P () c = π () c c sin t dt = sin t sin t dt = π + () t < = t < = c P S S = c g(t)f (t)dt S = π cos t cos t sin t sin t cos t cos t sin t+ sin t 4 9 π π π + π + 4 π π

9 () xy x OA t AO π + t AO t AP AP (π + t) t = π t y OP = OA + AP P = (cos t, sin t) + (cos(π t), sin(π t)) = (cos t, sin t) + ( cos t, sin t) = (cos t cos t, sin t + sin t) f(t) = cos t cos t, g(t) = sin t + sin t O t t A π t x () < = t < = π < = cos t < = f(t) = cos t ( cos t ) ( = cos t 4 ) + 9 cos t = 4 f(t) 9 cos a = 4 f(a) = 9 () () f(c) = cos c + cos c + = (cos c )( cos c + ) = cos c =, g(c) = sin c + sin c cos c = sin c( + cos c) = sin c = cos c = < c < π cos c = c = π () c = π π sin t dt = π = cos t dt [t sin t ] π = π + π sin t sin t dt = = = 4 π [ (cos t cos t)dt ] π sin t sin t

10 () y S = = = π π π g(t)f (t)dt (sin t + sin t)( sin t + sin t)dt ( sin t + sin t sin t + sin t)dt sin t sin t sin t () O x π sin t dt = = π ( cos 4t)dt [t 4 sin 4t ] π = π ( S = π + ) + 4 ( + π ) = π O C C C C P C Q Q (, ) P (, ) x OQ θ < = θ < = π () QP P θ () P x () P x y (4) P

11 9 () x (), () 7%

高校生の就職への数学II

高校生の就職への数学II II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................